Advancing high-speed train gearbox durability:enhanced bearing load and contact stress through transition from helical to herringbone gears

High-speed trains typically utilize helical gear transmissions,which significantly impact the bearing load capacity and fatigue service performance of the gearbox bearings.This paper focuses on the gearbox bearings,establishing dynamic models for both helical gear and herringbone gear transmissions in high-speed trains.The modeling particularly emphasizes the precision of the bearings at the gearbox's pinion and gear wheels.Using this model,a comparative analysis is conducted on the bearing loads and contact stresses of the gearbox bearings under uniform-speed operation between the two gear transmissions.The findings reveal that the helical gear transmission generates axial forces leading to severe load imbalance on the bearings at both sides of the large gear,and this imbalance intensifies with the increase in train speed.Consequently,this results in a significant increase in contact stress on the bearings on one side.The adoption of herringbone gear transmission effectively suppresses axial forces,resolving the load imbalance issue and substantially reducing the contact stress on the originally biased side of the bearings.The study demonstrates that employing herringbone gear transmission can significantly enhance the service performance of high-speed train gearbox bearings,thereby extending their service life.

Experimental Research on the Surface Quality of Milling Contour Bevel Gears

Contour bevel gears have the advantages of high coincidence,low noise and large bearing capacity,which are widely used in automobile manufacturing,shipbuilding and construction machinery.However,when the surface quality is poor,the effective contact area between the gear mating surfaces decreases,affecting the stability of the fit and thus the transmission accuracy,so it is of great significance to optimize the surface quality of the contour bevel gear.This paper firstly analyzes the formation process of machined surface roughness of contour bevel gears on the basis of generating machining method,and dry milling experiments of contour bevel gears are conducted to analyze the effects of cutting speed and feed rate on the machined surface roughness and surface topography of the workpiece.Then,the surface defects on the machined surface of the workpiece are studied by SEM,and the causes of the surface defects are analyzed by EDS.After that,XRD is used to compare the microscopic grains of the machined surface and the substrate material for diffraction peak analysis,and the effect of cutting parameters on the microhardness of the workpiece machined surface is investigated by work hardening experiment.The research results are of great significance for improving the machining accuracy of contour bevel gears,reducing friction losses and improving transmission efficiency.

Research on Cavitation Characteristics and Influencing Factors of Herringbone Gear Pump

Cavitation is a common issue in pumps,causing a decrease in pump head,a fall in volumetric efficiency,and an intensification of outlet flow pulsation.It is one of the main hazards that affect the regular operation of the pump.Research on pump cavitation mainly focuses on mixed flow pumps,jet pumps,external spur gear pumps,etc.However,there are few cavitation studies on external herringbone gear pumps.In addition,pumps with different working principles significantly differ in the flow and complexity of the internal flow field.Therefore,it is urgent to study the cavitation characteristics of external herringbone gear pumps.Compared with experimentalmethods,visual research and cavitation area identification are achieved through computation fluid dynamic(CFD),and changing the boundary conditions and shape of the gear rotor is easier.The simulation yields a head error of only 0.003%under different grid numbers,and the deviation between experimental and simulation results is less than 5%.The study revealed that cavitation causes flow pulsation at the outlet,and the cavitation serious area is mainly distributed in the meshing gap and meshing area.Cavitation can be inhibited by reducing the speed,increasing the inlet pressure,and changing the helix angle can be achieved.For example,when the inlet pressure is 5 bar,the maximumgas volume fraction in themeshing area is less than 50%.These results provide a reference for optimizing the design and finding the optimal design parameters to reduce or eliminate cavitation.

Application of Isogeometric Analysis Method in Three-Dimensional Gear Contact Analysis

Gears are pivotal in mechanical drives,and gear contact analysis is a typically difficult problem to solve.Emerging isogeometric analysis(IGA)methods have developed new ideas to solve this problem.In this paper,a threedimensional body parametric gear model of IGA is established,and a theoretical formula is derived to realize single-tooth contact analysis.Results were benchmarked against those obtained from commercial software utilizing the finite element analysis(FEA)method to validate the accuracy of our approach.Our findings indicate that the IGA-based contact algorithmsuccessfullymet theHertz contact test.When juxtaposed with the FEA approach,the IGAmethod demonstrated fewer node degrees of freedomand reduced computational units,all whilemaintaining comparable accuracy.Notably,the IGA method appeared to exhibit consistency in analysis accuracy irrespective of computational unit density,and also significantlymitigated non-physical oscillations in contact stress across the tooth width.This underscores the prowess of IGA in contact analysis.In conclusion,IGA emerges as a potent tool for addressing contact analysis challenges and holds significant promise for 3D gear modeling,simulation,and optimization of various mechanical components.

Contact Stress Reliability Analysis Model for Cylindrical Gear with Circular Arc Tooth Trace Based on an Improved Metamodel

Although there is currently no unified standard theoretical formula for calculating the contact stress of cylindrical gears with a circular arc tooth trace(referred to as CATT gear),a mathematical model for determining the contact stress of CATT gear is essential for studying how parameters affect its contact stress and building the contact stress limit state equation for contact stress reliability analysis.In this study,a mathematical relationship between design parameters and contact stress is formulated using the KrigingMetamodel.To enhance the model’s accuracy,we propose a new hybrid algorithm that merges the genetic algorithm with the Quantum Particle Swarm optimization algorithm,leveraging the strengths of each.Additionally,the“parental inheritance+self-learning”optimization model is used to fine-tune the KrigingMetamodel’s parameters.Following this,amathematicalmodel for calculating the contact stress of Variable Hyperbolic Circular-Arc-Tooth-Trace(VH-CATT)gears using the optimized Kriging model was developed.We then examined how different gear parameters affect the VH-CATT gears’contact stress.Our simulation results show:(1)Improvements in R2,RMSE,and RMAE.R2 rose from0.9852 to 0.9974(a 1.22%increase),nearing 1,suggesting the optimized Kriging Metamodel’s global error is minimized.Meanwhile,RMSE dropped from3.9210 to 1.6492,a decline of 57.94%.The global error of the GA-IQPSO-Kriging algorithm was also reduced,with RMAE decreasing by 58.69%from 0.1823 to 0.0753,showing the algorithm’s enhanced precision.In a comparison of ten experimental groups selected randomly,the GA-IQPSO-Kriging and FEM-based contact analysis methods were used to measure contact stress.Results revealed a maximum error of 12.11667 MPA,which represents 2.85%of the real value.(2)Several factors,including the pressure angle,tooth width,modulus,and tooth line radius,are inversely related to contact stress.The descending order of their impact on the contact stress is:tooth line radius>modulus>pressure angle>tooth width.(3)Complex interactions are noted among various parameters.Specifically,when the tooth line radius interacts with parameters such as pressure angle,tooth width,and modulus,the resulting stress contour is nonlinear,showcasing amultifaceted contour plane.However,when tooth width,modulus,and pressure angle interact,the stress contour is nearly linear,and the contour plane is simpler,indicating a weaker coupling among these factors.

Stability Analysis of Nonlinear Models of Nose Landing Gear Shimmy

Shimmy can reduce the service life of the nose landing gear, affect ride comfort, and even cause fuselage damage leading to aircraft crashes. Taking a light aircraft as the research object, the torsional freedom of landing gear around strut axis and lateral deformation of tire are considered. Since the landing gear shimmy is a nonlinear system, a nonlinear mechanical model of the front landing gear shimmy is established. Sobol index method is proposed to analyze the influence of structural parameters on the stability region of the nose landing gear, and Routh-Huritz criterion is used to verify the reliability of the analysis results of Sobol index method. We analyse the effect of torsional stiffness of strut, caster length, rated initial tire inflation pressure, rake angle, and vertical force on the stability region of theront landing gear. And the research shows that the optimization of the torsional stiffness of the strut and the caster length of the nose landing gear should be emphasized, and the influence of vertical force on the stability region of the nose landing gear should be paid attention to.

Research on Instantaneous Angular Speed Signal Separation Method for Planetary Gear Fault Diagnosis

Planetary gear train is a critical transmission component in large equipment such as helicopters and wind turbines. Conducting damage perception of planetary gear trains is of great significance for the safe operation of equipment. Existing methods for damage perception of planetary gear trains mainly rely on linear vibration analysis. However, these methods based on linear vibration signal analysis face challenges such as rich vibration sources, complex signal coupling and modulation mechanisms, significant influence of transmission paths, and difficulties in separating damage information. This paper proposes a method for separating instantaneous angular speed (IAS) signals for planetary gear fault diagnosis. Firstly, this method obtains encoder pulse signals through a built-in encoder. Based on this, it calculates the IAS signals using the Hilbert transform, and obtains the time-domain synchronous average signal of the IAS of the planetary gear through time-domain synchronous averaging technology, thus realizing the fault diagnosis of the planetary gear train. Experimental results validate the effectiveness of the calculated IAS signals, demonstrating that the time-domain synchronous averaging technology can highlight impact characteristics, effectively separate and extract fault impacts, greatly reduce the testing cost of experiments, and provide an effective tool for the fault diagnosis of planetary gear trains.

Research on Three-Dimensional Simulation of the Internal Arc Gear Skiving

Aiming at the problems that the simulation accuracy which is reduced due to the simplification of the model,a three-dimensional simulation method based on solid modeling is being proposed.By analyzing the motion relationship and positional relationship between the caries knife and the workpiece,the coordinate system of the caries machining was established.With the MATLAB software,the cutting edge model and the blade sweeping surface model of the boring cutter are sequentially established.Boolean operation is performed on the blade swept surface formed by the tooth cutter teeth with time t and the workpiece tooth geometry as well as the undeformed three-dimensional chip geometry model and the instantaneous cogging geometry model are obtained at different times.Through the compare between gear end face simulation tooth profile and the theoretical inner arc tooth profile,we verified the accuracy and rationality of the proposed method.

Time-Varying Mesh Stiffness Calculation and Dynamic Modeling of Spiral Bevel Gear with Spalling Defects

Time-varying mesh stiffness(TVMS)is a vital internal excitation source for the spiral bevel gear(SBG)transmission system.Spalling defect often causes decrease in gear mesh stiffness and changes the dynamic characteristics of the gear system,which further increases noise and vibration.This paper aims to calculate the TVMS and establish dynamic model of SBG with spalling defect.In this study,a novel analytical model based on slice method is proposed to calculate the TVMS of SBG considering spalling defect.Subsequently,the influence of spalling defect on the TVMS is studied through a numerical simulation,and the proposed analytical model is verified by a finite element model.Besides,an 8-degrees-of-freedom dynamic model is established for SBG transmission system.Incorporating the spalling defect into TVMS,the dynamic responses of spalled SBG are analyzed.The numerical results indicate that spalling defect would cause periodic impact in time domain.Finally,an experiment is designed to verify the proposed dynamic model.The experimental results show that the spalling defect makes the response characterized by periodic impact with the rotating frequency of spalled pinion.

Design of Pinion Machine Tool-settings for Spiral Bevel Gears by Controlling Contact Path and Transmission Errors

This paper proposes a new approach to design pinion machine tool-settings for spiral bevel gears by controlling contact path and transmission errors. It is based on the satisfaction of contact condition of three given control points on the tooth surface. The three meshing points are controlled to be on a predesigned straight contact path that meets the pre-designed parabolic function of transmission errors. Designed separately, the magnitude of transmission errors and the orientation of the contact path are subjected to precise control. In addition, in order to meet the manufacturing requirements, we suggest to modify the values of blank offset, one of the pinion machine tool-settings, and redesign pinion ma- chine tool-settings to ensure that the magnitude and the geometry of transmission errors should not be influenced apart from minor effects on the predesigned straight contact path. The proposed approach together with its ideas has been proven by a numerical example and the manufacturing practice of a pair of spiral bevel gears.

GEOMETRIC MODELING OF GENERATING-MANUFACTURED SPIRAL BEVEL GEARS BASED ON CUTTING SIMULATION

A geometric modeling method for generating-manufactured spiral bevel gears（SBGs） is proposed. It consists of two steps： （1） creating a reference model by simulating the process of cutting spiral bevel gear,（2） reconstructing the final solid model by collecting data points from the reference model and fitting these points into NURBS surfaces. In this method,cutting simulation avoids abstruse mathematical theories and complex methods,thus making it convenient to obtain data points on the complex tooth surface before the gear is manufactured and efficient to increase the accuracy of the solid model. Also,the representations of tooth surfaces of the final model is unified as a NURBS surface function. The NURBS surface is continuous and smooth,thus it is available for wide applications in CAD/CAE. The experiment proves that the method can be used to establish an accurate pair of SBG models,thus providing a feasible and effective way for CAD/CAE modeling.

一种基于Gears离线存储的Web测评系统实现研究

本文主要以我院承担的一项省级重点科研项目"高职教学手段网络化支持系统的研究与应用"为依托,重点就测评子系统中试卷的客户端存储问题进行分析和讨论,并给出了一个基于GoogleGears技术的可行的解决方案.

Statistical Modification Analysis of Helical Planetary Gears based on Response Surface Method and Monte Carlo Simulation

Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system＇s dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error（DTE） fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system＇s dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.

Geometry Design and Tooth Contact Analysis of Crossed Beveloid Gears for Marine Transmissions

Beveloid gears,also known as conical gears,gain more and more importance in industry practice due to their abilities for power transmission between parallel,intersected and crossed axis.However,this type of gearing with crossed axes has no common plane of action which results in a point contact and low tooth durability.Therefore,a geometry design approach assuming line contact is developed to analyze the tooth engagement process of crossed beveloid gears with small shaft angle for marine transmission applications.The loaded gear tooth contact behavior is simulated by applying a quasi-static analysis to study the effects of gearing parameters on mesh characteristics.Using the proposed method,a series of sensitivity analyses to examine the effects of critical gearing parameters such as shaft angle,cone angle,helix angle and profile-shift coefficient on the theoretical gear mesh is performed.The parametric analysis of pitch cone design shows that the dominant design parameters represented by the angle between the first principle directions（FPD） and normal angular factor are more sensitive to the shaft and cone angles than they are to the helix angle.The theoretical contact path is highly sensitive to the profile-shift coefficient,which is determined from the theoretical tooth contact analysis.The FPD angle is found to change the distribution of contact pattern,contact pressure and root stress as well as the translational transmission error and the variation of the mesh stiffness significantly.The contact pattern is clearly different between the drive and coast sides due to different designed FPD angles.Finally,a practical experimental setup for marine transmission is performed and tooth bearing test is conducted to demonstrate the proposed design procedure.The experimental result compared well with the simulation.Results of this study yield a better understanding of the geometry design and loaded gear mesh characteristics for crossed beveloid gears used in marine transmission.

COMMON DEFINITION FOR END-SURFACE CONTACT RATIO OF GEARS AND ITS APPLICATIONS

Common definition and calculating expressions of end-surface contact ratiofor all type of gears are put forward, and with calculation expressions for involute gears,micro-segments profile gears, and sine-curved profile gears being discussed. The end-surface contactratio of gears is defined as the ratio of the action angle (the rotation angle of gear from gear-into gear-out for one pair of teeth) to the rotation angle per pitch (or central angle per tooth).According to the theory of gearing, equation of the meshing line can be deduced from the toothprofiles of basic rack. Having obtained the equation of the meshing line, and being given theaddendum outline of the gears, the contact ratio can be calculated with the calculation expressions.For the involute gears, this definition has same effect as the well-known definition: ratio of thecontact line to the base pitch. This definition of contact ratio is also suitable to othernon-involute gears, such as micro-segments profile gears, sine-curved profile gears, and can givemore reliable results.

Optimum Weight Design of Functionally Graded Material Gears

Traditional gear weight optimization methods consider gear tooth number, module, face width or other dimension parameters of gear as design variables. However, due to the complicated form and geometric features peculiar to the gear, there will be large amounts of design parameters in gear design, and the influences of gear parameters changing on gear trains, transmission system and the whole equipment have to be taken into account, which increases the complexity of optimization problem. This paper puts forward to apply functionally graded materials（FGMs） to gears and then conduct the optimization. According to the force situation of gears, the material distribution form of FGM gears is determined. Then based on the performance parameters analysis of FGMs and the practical working demands for gears, a multi-objective optimization model is formed. Finally by using the goal driven optimization（GDO） method, the optimal material distribution is achieved, which makes gear weight and the maximum deformation be minimum and the maximum bending stress do not exceed the allowable stress. As an example, the applying of FGM to automotive transmission gear is conducted to illustrate the optimization design process and the result shows that under the condition of keeping the normal working performance of gear, the method achieves in greatly reducing the gear weight. This research proposes a FGM gears design method that is able to largely reduce the weight of gears by optimizing the microscopic material parameters instead of changing the macroscopic dimension parameters of gears, which reduces the complexity of gear weight optimization problem.

Pinion Tooth Surface Generation Strategy of Spiral Bevel Gears

Aviation spiral bevel gears are often generated by spiral generated modified（SGM） roll method.In this style,pinion tooth surface modified generation strategy has an important influence on the meshing and contact performances.For the optimal contact pattern and transmission error function,local synthesis is applied to obtain the machine-tool settings of pinion.For digitized machine,four tooth surface generation styles of pinion are proposed.For every style,tooth contact analysis（TCA） is applied to obtain contact pattern and transmission error function.For the difference between TCA transmission error function and design objective curve,the degree of symmetry and agreement are defined and the corresponding sub-objective functions are established.Linear weighted combination method is applied to get an equivalent objective function to evaluate the shape of transmission error function.The computer programs for the process above are developed to analyze the meshing performances of the four pinion tooth surface generation styles for a pair of aviation spiral bevel gears with 38/43 teeth numbers.The four analytical results are compared with each other and show that the incomplete modified roll is optimal for this gear pair.This study is an expansion to generation strategy of spiral bevel gears,and offers new alternatives to computer numerical control（CNC） manufacture of spiral bevel gears.

Filling Rules of Bevel Gears in the Closed-die Cold Forging

The closed-died cold forging technology of the bevel gears used in Jada car was investigated. With the analysis of the strain field and velocity field of the plastic deformation and the endured forces of the dies, the filling rules for the metal were analyzed by the elastic-plastic finite element method （FEM）. The results show that there is a great difference among closed-die cold forging, extrusion and forging, as far as the metal flowing is concerned. The outer addendum cannot be filled completely in the closed-die cold forging of the bevel gears, and the round angle will be formed. But it does not influence the application of the bevel gears. At the beginning, the rigid area is formed in the cavity of the lower die. And then it will move upwards to supply the metal for the gear filling. For the closed-die cold forging of the bevel gears, the force acting on the upper die and the lower die is significantly different.

NC METHOD FOR GENERATION OF CONJUGATING HYPOID GEARS BASED ON NC’S FLEXIBILITY

It is known that manufacture of hypoid gears is difficult and complicated,the reason lies on the limitation of traditional mechanical machine tools. With the development ofNC machine tools, there should be new ways of cutting this kind of gear. Therefore, an idea togenerate gears with conjugating tooth surfaces is proposed, based on the 'flexibility'characteristic of NC that means various motions, in a sense, can be performed, arbitrarily on NCmachine tools. Using this method, the direction of the contact path on tooth surfaces can becontrolled, and also, theoretically, the generated tooth surfaces can transmit motion at specifictransmission ratio curve.

Analysis and Optimization on Factors Affecting Forming Quality of Half Axle Gears Warm Precision Forging

Half axle gears is produced by precision forging popularly because of the advantages in minimum machining allowances, lower material consumption and good service properties. But the forming quality of precision forging is difficult to control. Many simulations and analysis of precision forging process were taken by previous researchers. But no concrete method is proposed to evaluate and optimize the forming quality of half axel gears. The primary purpose of this work is improving the forming quality of half axel gears by analyzing and optimizing the affected factors of forming quality. The enclosed-die warm forging process of half axle gears was developed, and a new type of die-set used on double action hydraulic press was brought forward. The main influential factors of precision forming quality were analyzed after the forming process had been simulated by using finite element method（FEM）. These factors include die structure, web thickness and web position. A method used to evaluate the forming quality was established, which investigated the maximal forming load, the metal filling rate and the material damage factor. The FEM simulations of half axle gears precision forging were evaluated by this method. The results show that the best forming quality can be achieved when the punches were added with bosses, the web located at the middle plant of the gear, and the web thickness was 30 percent of the inner hole diameter. Verification experiments taking the above optimized parameters were performed on a 7.8 MN double action hydraulic press. The trial products were formed well. And their geometric precision meets the demand. The verification result shows that the optimization of the influential factors, according to the simulations and the evaluation method, can improve the forming quality. The new structure of precision forging die-set and the new evaluation method guarantee a high forming quality ofhalfaxel gears.